Question

Сos⁴ а +sin ⁴ a =1 -1/2 sin ² 2 а докажите тождество

Answer 1

$displaystyle cos^4alpha+sin^4alpha=underbrace{sin^4alpha+2sin^2alphacos^2alpha+cos^4alpha}_{(sin^2alpha+cos^2alpha)^2}-2sin^2alphacos^2alpha=\ \ =1^2-2sin^2alphacos^2alpha=1-dfrac{1}{2}left(underbrace{2sinalphacosalpha}_{sin2alpha}right)^2=1-dfrac{1}{2}sin^22alpha$